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deftaylor

Run Example
(%i1)deftaylor (f(x), cos(x)-cos(y) + sum(x^i/(2^i*i!^2), i, 4, inf));
(%o1)                                 [f]
(%i2) taylor (exp (sqrt (f(x))), x, 0, 4);
                                    %i sqrt(cos(y) - 1)                       2
           %i sqrt(cos(y) - 1)   (%e                    sqrt(cos(y) - 1) %i) x
(%o2)/T/ %e                    + ----------------------------------------------
                                                  4 cos(y) - 4
            %i sqrt(cos(y) - 1)
 - (((385 %e                    sqrt(cos(y) - 1) %i
         %i sqrt(cos(y) - 1)                 %i sqrt(cos(y) - 1)
 + 576 %e                   ) cos(y) + 191 %e
                             %i sqrt(cos(y) - 1)   4
 sqrt(cos(y) - 1) %i - 576 %e                   ) x )
           2
/(18432 cos (y) - 36864 cos(y) + 18432) + . . .
(%i3) 
Run Example
deftaylor (f(x), sum( ( ((-1)^n) * (x^(2*n+1)) ) / ((2*n+1)*(2*n+1)!), n, 0, 3));
(%o1)                                 [f]
(%i2) powerseries (f(x), x, 0);
                                7      5     3
                               x      x     x
(%o2)                       - ----- + --- - -- + x
                              35280   600   18
(%i3) g(x):= taylor (f(x), x, 0, 4);
(%o3)                    g(x) := taylor(f(x), x, 0, 4)
(%i4) integrate(g(x),x,0.1);
                                     2    4
                                    x    x
(%o4)                               -- - --
                                    2    72
(%i5) 
Run Example
deftaylor (f(x), x^2 + sum(x^i/(2^i*i!^2), i, 4, inf));
(%o1)                                 [f]
(%i2) 

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